An improved shear deformation theory for laminated shells Addressing transverse stress continuity

A layerwise shear deformation theory is developed to improve the accuracy of stress and strain prediction in the analysis of laminated shell structures. The in-plane displacement field is assumed using layerwise hyperbolic functions to accommodate complexity of zigzag in-plane warping and shear stress distribution. The assumed displacement field satisfies free transverse shear stress conditions on the top and the bottom surfaces of the laminate. The continuity of transverse shear stresses and in-plane displacements at interlamina surfaces is used to obtain the relations between layerwise structural variables. These relations, expressed in terms of laminate geometry and material properties, reduce the number of independent variables in the field description. Thus, the number of structural variables in the present model is independent of the number of laminae, which makes the model computationally efficient. The developed theory is implemented using finite element technique. To assess the accuracy of the present theory, the cylindrical bending of composite laminates, for which exact elasticity solutions exist, is investigated first. The correlation shows good agreement with exact solutions even for thick constructions. The cases of spherical laminated shells under point loading and uniformly distributed loading are investigated next. The results are compared with those obtained using classical laminate theory. As expected, good correlation is observed if thin constructions are used while significant deviations occur for thicker constructions. The developed two dimensional model provides an accurate and efficient framework for the analysis of laminated shell structures of arbitrary thickness.